Chapter 14
Simulation Modeling
What Is Simulation?
• Simulation is to mimic a process by
using computers.
Simulation and Decision Making
• Simulation helps pre-view a
complicated business process to
identify possible problems;
• It allows to try different decision
alternatives, and select the best
alternative as the decision.
Simulation and Uncertainty
• Simulation is particularly useful
when there exist uncertainties
(demand, processing time, for
example) in a process with many
correlated factors.
Probable Events and
Random Numbers
• Probable events:
– Tossing a coin, it may land on Head (0.5) or Tail
(0.5).
– Daily demand of an item can be 4 units (0.3), 5
units (0.45), or 6 units (0.25).
• Computers can randomly generate a number
between 0 and 1.
Simulate Tossing Coins
• A randomly generated number has 50%
chance between 0 and 0.5, 50% chance
between 0.5 and 1.
• So, we can simulate the result of tossing a coin
by generating a random number T so that if T
is between 0 and 0.5, then the result is
“Head”; if T is between 0.5 and 1, then the
result is “Tail”.
Simulate Probable Outcomes with
Random Numbers
• The key idea of simulating probable outcomes
with randomly generated number in
computer:
Probability of a possible actual outcome
=
Probability of the corresponding possible
outcome in computer simulation
Simulate Tossing a Dice
• Probability of landing on a number is 1/6.
• Computer randomly generated numbers are
uniformly spread over the range 0~1.
• Divide range 0~1 evenly into six parts, so that:
– (0 to 0.1667) for “landing with 1”;
– (0.1667 to 0.333) for “landing with 2”;
–…
– (0.8333 to 1) for “landing with 6).
Simulate Daily Demands
• Possible demands 40, 50, 60 units with
probabilities 0.2, 0.5, 0.3 respectively.
• Divide range 0~1 into three parts with lengths
0.2, 0.5, and 0.3 respectively.
• If a random number is between 0 and 0.2,
then demand is 40 units; between 0.2 and 0.7
then 50 units; between 0.7 and 1 then 60
units.
Simulate a Probable Event
• In general, to simulate probable outcomes
with randomly generated numbers:
Step 1. Put all possible outcomes and their
probabilities in a table;
Step 2. Calculate cumulative probabilities;
Step 3. Use the cumulative probabilities as the
cutting points of random number ranges.
=RAND()
• =RAND() is an Excel function generating a
random number between 0 and 1.
=IF()
• Syntax of =IF() function in Excel:
=IF(C,a,b)
It means: If condition C is true then the
function value is a, otherwise the value is b.
• e.g. For tossing coins:
=IF(C4>0.5, ”Head”, ”Tail”)
• =IF() function can be nested, e.g.
=IF(B5<0.2, 40, IF(B5<0.7,50, 60))
=VLOOkUP()
• If we use =IF() function to represent six
possible outcomes in tossing a dice case, then
we have to have get =IF() function nested for
five times, which is too awkward.
• =VLOOKUP() facilitates our work in that case.
• Syntax of =VLOOKUP():
=VLOOKUP(value to lookup, range table,2)
Range Table for =VLOOKUP()
• 1st column contains separating points of
ranges
– Start from the smallest allowable number of the
ranges
– In ascending order
• 2nd column lists values of =VLOOKUP
corresponding to the ranges.
=VLOOKUP() for Tossing Dices (1)
• Set up the table of ranges.
– Cumulative probabilities are in the 1st column,
starting from 0
– Possible outcomes are in the 2nd column.
B
5
6
7
8
9
10
11
12
C
Cumu. Prob Values
0
1
0.1667
2
0.3333
3
0.5
4
0.6667
5
0.8333
6
1
=VLOOKUP() for Tossing Dices (2)
• Generate the simulation table:
– In F5: =RAND()
– In G5: =VLOOKUP(F5, $B$6:$C$12, 2)
– Copy E5, F5, and G5 down to other rows.
2
3
4
5
6
7
E
F
G
Simulation of tossing dices
Tossing
#
1
2
Random Outcome
number of tossing
0.618707
4
Simulate Demands (1)
• Possible daily demands (from past data):
Demand
8
Probability
0.01
9
0.06
10
11
12
13
0.11
0.34
0.31
0.10
14
0.05
15
0.02
Simulate Demands (2)
• Calculate Cumulative Probabilities:
Demand
8
Probability
0.01
Cumulative Probability
0.01
9
0.06
0.07
10
11
12
13
0.11
0.34
0.31
0.10
0.18
0.52
0.83
0.93
14
0.05
0.98
15
0.02
1.00
Simulate Demands (3)
• Generate Vlookup range table in Excel
E
F
Cumulative
Probability Demand
4
5
6
7
8
9
10
11
12
0
0.02
0.07
0.18
0.52
0.83
0.93
0.98
1
8
9
10
11
12
13
14
15
Simulate Demands (4)
• Generate Simulations in Excel
– In B4: =RAND()
– In C4: =VLOOKUP(B4,$E$4:$F$12,2)
– Copy A4, B4, C4 down to other rows
A
3
4
5
6
B
C
Random
Day #
Demand
number
1
0.575409
12
2
3
Tips of using Excel
• Use cell addresses, relative or absolute, rather
than the values in the cells;
• Use Copy / Paste functions as far as possible;
• Use multiple columns to decompose
complicated formulas;
• Put the parameters to be changed on the top
of the spreadsheet;
• Put the summary results on top.
Simulation for Decision Making
• A simulation is actually a description of
day-by-day or week-by-week business
operations.
• For a decision alternative, the simulation
shows its effects on business quality
or/and profit.
• After trying alternatives, the manager
can pick one that would be best for
business.
How Many Cases to Stock? (1)
• Product BC-6 costs $56.95/case from the supplier, and is sold
at the price of $91.80/case. For the cases unsold at the end
of a week, the store will sell them to a convenient store at
price of $12.50/case. Shortage penalty cost is about $4 per
case short. Possible demands of a week and their
probabilities are as follows from the past records:
Weekly demand of BC-6
Probability
11 cases
0.45
12 cases
0.35
13 cases
0.2
• Manager Wendy is considering how many cases of product
BC-6 to stock at beginning of each week.
Simulations of Weekly Business Operations on BC-6
Selling price ($):
Salvage value ($):
Order cost ($):
Goodwill penalty ($):
91.80 per case
12.50 per case unsolde at the end of a week
56.95 per case
4.00 per case short
Number of cases of BC-6 to stock every week:
Total number of cases shortage in 52 weeks:
Total number of cases surplus in 52 weeks:
Total profit in 52 weeks:
Average weekly profit of 52 weeks:
12
<- enter your trial order quantity in cases
14
18
20,263.00
389.67
Goodwill
Revenue
Revenue of
penalty
Number
Numbr
of the Number of
Number the week
Total
Total
Total
Weekly
in the
Week of cases Random
of cases
week
cases
of cases from selling revenue cost of profit of
Demand
week due
#
ordered
#
sold in
from
short in
surplus in surplus at
of the the week the week
(case)
to
per week
the week regular the week
the week salvage
week ($)
($)
($)
shortage
sales ($)
price ($)
($)
1
12
0.527107
12
12
1101.6
0
0
0
0
1101.6
683.4
418.2
2
12
0.951569
13
12
1101.6
1
4
0
0
1101.6
687.4
414.2
3
12
0.059013
11
11
1009.8
0
0
1
12.5
1022.3
683.4
338.9
4
12
0.967144
13
12
1101.6
1
4
0
0
1101.6
687.4
414.2
5
12
0.466342
12
12
1101.6
0
0
0
0
1101.6
683.4
418.2
6
12
0.070006
11
11
1009.8
0
0
1
12.5
1022.3
683.4
338.9
How Simulation Helps Decide How
Many Cases to Stock (3)
• The worksheet each time simulates 52
weeks of business operations.
• Given the number of cases to order (green
cell), Excel gives the operation results of 52
weeks (yellow cells).
• Decision maker may change the green cell,
observe the outcome of 52 weeks in yellow
cells, and choose the best order quantity.
Inventory Simulation (1)
• An inventory simulation simulates day-by-day
transactions occurred on inventory, such as
daily demand of inventoried item, number of
units in stock, placing an order, length of lead
time, and costs involved.
• An inventory simulation helps determine
when to place an order to the supplier and
how many units in an order.
Inventory Simulation of 365 days
Ordre Quantity:
Reorder Point:
Total
Day
0
1
2
3
4
5
6
7
8
750
15099
Units Begin on
received
hand
0
25
0
25
0
21
0
16
0
12
0
8
0
3
0
0
150
150
150
10
97.195
Cost H per day: 0.05
Cost S per order: 25
Cost L.S. / unit: 20
758
25
14366
Total holding:
Total setup:
Total L.S. cost:
Overall total:
750
718.3
125
500
1343.3
3.0048
Lost Ending
Order
Rand # Demand sales on hand Order? Quantity Rand #
0
0
25
0
0.6682
4
0
21
N
0
0.9004
5
0
16
N
0
0.5151
4
0
12
N
0
0.3733
4
0
8
Y
150
0.5057
0.8038
5
0
3
N
0
0.9435
6
3
0
N
0
0.7776
5
5
0
N
0
0.5561
4
0
146
N
0
16
34
Lead
Time
Lead time
Remaining
0
0
0
0
3
2
1
0
0
0
0
0
3
0
0
0
0
How Simulation Helps Make
Inventory Decision (3)
• For each “re-order point” and “order
quantity” tried, the simulation shows the total
inventory cost (including holding cost,
ordering cost, and lost sales cost) of a year.
• A good re-order point (showing when to place
an order) and a good order quantity (showing
many units in an order) can thus be selected
from many alternatives.
Other Examples of Business
Simulations with Excel
•
•
•
•
•
•
Minutes-by-minutes waiting lines;
Gambling game;
Production in a workshop;
Transactions in a bank;
Truck transportation;
Department store operations to see the
requirements of resources.